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Patented
2,411,916
3,1946 ' '
; UNITED STATES PATENT OFFICE
MEASURING APPARATUS
John R. 'Woodyard, Garden City, N; Y., assignor
to Sperry Gyroscope Company, Inc., a corpora
tion of New York
Application June 28, 1943, Serial No. 492,573
11 Claims. (01. ‘172-245)
1
nating. quantities is modulated with the other to
My invention relates to electrical measuring
devices in general, and more particularly to meth
ods and apparatus for determining the phase an;
gle'between two alternating or periodically vary;
ing quantities.
'
produce a direct current proportional to a func
tion of the ‘phase angle between them.
‘
The alternating quantities are recti?ed in an
5 other branch of the circuit by means of full-wave
An object of my invention is to provide a de
- recti?er-s and impressed on the signal and car- '
rier terminals of a second balanced modulator,
the output of which is proportional to the product
or the two periodically varying quantities.‘ The
restoring force acting on the indicating element
10 outputs of each of the balanced modulators are
thereof is independent of frequency.
then delivered‘ to a quotient-taking device where
Another object of myinvgention is to provide an
the quotient of the two modulated outputs is
electronic phase meter which is less affected by
taken to give an indication of the phase angle to
noise or other random ?uctuations than are .prior
vice for measuring the phase difference between
two periodically varying quantities in which the
electronic phase meters.
'
vbedetermined.
-
-
.
It is also ancbject of my invention to provide‘ 15 ' ' vA more comprehensive understanding of my in
vention will be afforded from the following de
a phase meter which utilizes the information of
tailed description when taken together with the
the impressed signal quantities over whole cycle
periods.
'
_
accompanying drawing in which, .
_
Another purpose of my invention'is to provide
a method and apparatus forv determining the 20
phase angle between two alternating electrical
'
d
Fig. 1 is a circuit diagram of‘ an embodiment
of my invention;
'
'
Fig. 2 is a modified block diagram of the cir- f
quantitiesin which a product of the two is divided
cuit shown inF-ig. 1; and
by another product, obtained by multiplying the
Fig. 31s a schematic diagram showing‘the op
eration of the balanced modulators used in Fig. 1.
two quantities after recti?cation, to give a meas
urement of phase di?erence.
,
25 - As indicated schematically in Fig. 2; the illus
'
trated apparatus comprises a pair of balanced
Another purpose of myv invention is to provide
a phase meter in which no moving parts carry
the quantities whose phase di?erence is to be
modulators l3 and 80, each of which is made re
sponsive .to both of‘ the vector voltages Eli and
E2, which are to be compared in phase. The
A still further object ‘of- my invention is to ar 30 modulator I3 is directly connected to the voltage
range in an electronic phase-measuring circuit
inputs E1 and E2 so as to yield an output propor
two balanced modulators, which produce direct
tional to the vector product of the input voltages,
current outputs» respectively proportional to a
which includes, the .phase angle factor, cos 0. On
function of the phase angle between the two quan
. the other hand, the balanced modulator 60 has
.tities whose phase- di?erence is to be determined 35 recti?ers 3i and 43, respectively, interposed in
and to their product, and a device such as a
the inputconnections from the voltages E1 and
crossed-coil ‘ohmmeter which is capable of tak
E: so that phase-effect is eliminated and‘ 'D.-C.
ing the quotient of the two direct currents so pro
voltages representing scalar values E1 and E: are
duced, to give an indication of the phase angle.
Yet another purpose of my invention isto pro 40 supplied to the balanced modulator 60 rendering
it responsiveto the scalar product of the volt
vvide a method for determining the phase angle
ages. The ratio instrument ‘His provided, which
between two periodically varying electrical quan
has input connections from the output of the. ele
titles in which two direct currents are produced
ments i3 and 60 for producing a phase angle
'. therefrom by modulation and recti?catiodwhich
measured.
I
'
are proportional to a function of the phase angle
between the quantities and to their products, the
quotient of the direct current quantities being
45
indication.
,
v
, In the embodiment of my invention illustrated
more in detail in Fig. 1, I provide two pairs of in
put terminals“ and II which receive the alter~
'nating quantities whose phase angles'are to be‘
Other objects of my invention will become a'p-' 50 compared.
taken to give an indication of phase angle meas
urement.
,
._
'
From input terminals ll, the'quantity.v im
parent and those listed more evident as the de
scription proceeds.
'
.
.
'
In practising my invention, in a preferred em
bodiment thereof, Iprovide a circuit having two
pressed thereon is conducted to transformer 14
whose tapped secondary forms the balanced cir
cuit of balanced modulator i3; comprising the '
pairs of input terminals, each of which receives 55 electronic discharge devices i1 and I8, illustrated
one of the two alternating quantities whose phase
angle difference is to be measured. From these
as triodes.
input terminals the electrical quantities are de- -
coupled in the cathode circuit of balanced modu-~ . '
Transformer IS; the secondary of which is
lator l3, receives the electrical quantity impressed
livered to the'signal and carrier input terminals
of a balanced modulator where one of the ‘alter 60 upon input terminals I2.v Controlv grids i9 and
2,411,916
3
' 24 of elements 11 and I8 receive signal voltages
from the secondary winding of transformer 14
which are used to modulate the output of trans
.former l5. The secondary of this transformer
15 is in series with energy source 16 and together
1 these elements form a circuit for connecting
spective quantities are recti?ed to produce scalar
quantities E1 and E2 which are delivered to bal
anced modulator 60 operating as a product-tak
ing circuit. The output of this last-mentioned
circuit, proportional to the product ElEZ, and the
current proportional to the product EIEZ cos 0, are
cathodes 22 and 23 of elements 11 and 18 to the
\mid-point of the secondary winding of trans
former
l4.
_
4
Within the recti?ers 3| and 43, each of the re
delivered to a quotient-taking device 14 where
division of the two quantities is made to give an
_
Plates 2| and 25 of these elements deliver the 10 indication of 0.
In operation, the balanced modulators l3 and,
output of balanced modulator 13 to resistors 29
60 and the full-wave recti?ers 3| and 43 function
and 30 and receive positive voltage from source
normally and, accordingly, a detailed explanation
28. By-pass capacitors'26 and 21 are coupled in
of their operation will not be made. A theoretical
parallel with elements 11 and I8, respectively, for
by-passing the alternating components of their 15 analysis of the operation of the balanced modu
lator, with modulator l3 taken as an example,
respective outputs.
will be presented to explain the theory'of the
The signal received on input terminals H is
invention.
\
also delivered to the primary winding of trans
Referring to Fig. 3 and using the series expan
former 32 which, together with the electronic
discharge elements 33 and 34, comprises the full 20 sion for electrode currents, the plate current ii
of tube 11 may be expressed as
wave recti?er 3i. Anodes 35 and 31 of elements
33 and 34, both of which are illustrated as diodes,
receive the output of the secondary winding of
‘and the plate current i2 of tube l8 as
transformer 32 and their cathodes 36 and 38
deliver the output of the recti?er to a ?ltering 25
circuit comprising a resistor 39 and capacitors 4|
Where the a’s are constants, the value of each de
and 42. The output of full-wave recti?er 3| is
pending upon tube characteristics and external
delivered to the signal input terminals of balanced
circuits, and ea and er are the instantaneous
modulator 60, which in turn delivers it to the con
trol grids 62 and 66 of elements 59 and 5!, com 30 values of signal and carrier voltages respectively,
whose values may be expressedvas
prising a part of balanced modulator 60.
The electrical quantity received on the input
(3)
8a==Ei sin wt
terminals l2 passes through the primary winding
and
of transformer 44 and is induced in the secondary
‘ _ winding thereof for delivery to anodes 41 and 49
(4)
8b=E2 sin (wt-9)
of elements 45 and 4B in the ‘full-wave recti?er
where 6 is the phase angle between E1 and E2.
43. The output of this last-mentioned device is
The resultant current ‘it delivered to terminals
taken from cathodes 48 and 5| and delivered to
15 and 16 is therefore equal to the algebraic sum
a ?ltering circuit comprising capacitor 52, resistor
of the currents i1 and i: or
53, and capacitor 54. Through‘the ?ltering cir 40
(5)
cuit last mentioned the output of the full-wave
recti?er 43 is delivered to the balanced modulator
which in terms of Equations ‘1 aid 2 may be
50 across the resistor 51.
expressed as
The output of balanced modulator 60, in the
form of a direct current proportional to E1E2 is
delivered from plates 63 and 61 of elements 59
'
By choosing the'proper operating voltages for
the tubes 11 and i8, all components higher than
the second order will be made negligible and
and 5| to the resistors 12 and 13.‘ 'Plate current -
is supplied the elements of balanced modulator
60 from source 1| and the grids thereof are biased
from voltage source 58. By-pass capacitors 68
and 69 are coupled in the output circuit of bal
anced modulator 60 for by-passlng .A. 0. com
'
ponents.
The direct current outputs of balanced modu
lators I3 and 60 are delivered to a quotient-taking
device 14, which is illustrated. as a crossed-coil
ohmmeter and which is calibrated to give an in
a1
dication of the phase angle existing between the
two voltages impressed upon input terminals II
and I2.
-
60
While element 14 is illustrated as a crossed-coil
ohmmeter it may take the form of any ratiometer
or quotient-taking device, such as an Evershed
“Meg'ger,” or may be of the electronic type in
which electronic discharge-elements having log- .
arithmic characteristic curves are used.
With reference to Fig. 2, the operation of the
circuit may be explained from a functional stand
.point in the following manner:
The vector quantity 1111 representing one of the ’
two alternating quantities, between which the
phase angle difference is to be determined, is re
ceived by balancedmodulator l3 where it modu
lates the quantity 112 to produce a direct current
output proportional to the quantity E1E2 cos 0. 75
Substituting the values of es and en, expressed
by Equations 3 and 4, in Equation 8 and collect
ing terms
Since the alternating current components of
the output current in of balanced modulator 13
are by-passed by capacitors 25 and 21, the direct
current indc delivered to" terminals 15 and 16,
as de?ned by the second term of Equation 9, is
(10)
iode=2d2E1E2 cos 0
and is proportional to EIEZ cos 0.
‘
4
By similar analysis as evidenced by Equation 9
developed above, it is seen that the output iudc
of balanced modulator 80 is proportional to the ‘
product EiEz, ‘and when combined by suitable
means with the output of balanced modulator
2,411,910
6
'
.
i3, expressed by Equation 10, a quantity pro
trical quantities varying in phase with each other
portional to cos 0 is obtained and through proper
callbration may be indicated as the angle 0.
Modi?cations in my invention are. of course,
possible and may suggest themselves in ‘view of
by an angle 0, means for producing from said al
ternating electrical quantities a ?rst direct, cur
rent proportional‘to a function of said angle 0,
means for producing from said alternating elec
trical quantities a second direct current propor
tional to their-product, and means for taking the
quotient of said ?rst and said second direct cur
the foregoing disclosures. Accordingly, the spirit
and-scope’of my invention is to be limited only
by the appended claims.
'
What is claimed is: ~
rents to give an indication of the value of said
_
1. Apparatus for determining the phase rela* -1D
tionship between two periodically varying elec
angle 0.
/
.
.
trical quantities, comprising means for modulat- '
7. A method for measuring the phase diiference
between two alternating electrical quantities,
ing one of said quantities with the other, means
comprising the steps of modulating one of said
for rectifying each of said periodically varying ' quantities with the other to produce a-product
quantities, means for modulating said recti?ed 15 thereof, converting each of said alternating
electrical quantities into unidirectional quanti
electrical quantities one with the other, and
ties, combining said unidirectional quantities to
means for receiving the outputs of the respective
produce a product thereof, and combining both
modulating means to give an indication of-phase.
of said products so produced to give an indiy
2. In an electronic phase meter, a ?rst bal
anced modulator for modulating one of two 20 cation of phase angle.
8. Av method of measuring the phase angle
- periodically varying electrical quantities with ‘the
other, separate recti?ers for rectifying each of .' ‘ between two periodically v'aryi'ngelectrical quan
said periodically varying quantities, a second‘
. titles, comprising the stepsv of multiplying one
» balanced modulator for modulating the output
with the other to obtain a ?rst product, rectifying
each of said periodically varying electrical quan
titles to produce two unidirectional quantities,
multiplying one of said unidirectional quantities
of one of said recti?ers with'the output of the
other, and means for determining the quotient _
of the outputs of said ?rst and second modulators ,
to give an indication of phase angle. '
3. In an electronic phase meter a circuit having
with the other to produce a second product, com
bining said ?rst and second products to produce )
‘.wo pairs of input terminals each of which re-. 30 an electrical quantity proportional to the phase
angle between the two periodically varying elec
ceive one of‘ two periodically varying electrical
trical quantities, and measuring said last-men
quantities, a balanced modulator for modulating.
tioned electrical quantity to give an indication of
one of said quantities with the other, first and *~
phase angle.
4
second full-wave rectifying‘ devices for rectifying
9. A method for determining the difference in
each of said periodically varying electrical quan 35
phase between'two alternating electrical quanti
tities, a balanced modulator-for modulating the
ties, comprising the steps of modulating one of
output of said ?rst full-wave recti?er with the
said quantities with the other to produce a ?rst
output of said second full-wave recti?er, and
means including a crossed-coil ratiometer for re
. modulated quantity, rectifying each of said alter
ceiving the outputs of said balanced‘ modulators 40 nating electrical quantities to produce ?rst and .
to give an indication of the phase angle between '
second recti?ed electrical quantities, modulating
said ?rst recti?ed electrical quantity with said
second recti?ed electrical quantity to produce a
second modulated quantity, and taking the quo
‘ 4. Apparatus for measuring the phase relation
ship between two periodically varying electrical v 45 tient of said ?rst and second modulated quanti
ties to give an indication of phase angle.
quantities, comprising means for taking the
10. A method for determining the phase angle
product of said periodically varying electrical‘
quantities, means for rectifying each of said‘ ' between two periodically ‘varying electrical quan
tities, comprising the steps of producing a ?rst
periodically varying electrical quantities to pro
. direct current from said periodically varying elec
duc a plurality of recti?ed outputs, means for
trical quantities proportional'to a function of the
taking the product of said recti?ed outputs, and
phase angle between them, producing a second
means for dividing one product by the other to
direct current from said periodically varying elec
measure the phase angle between said periodically
the two quantities impressed on the input
terminals of the circuit.
'
_
'
varying electrical quantities.
'
.
'
i
‘
trical quantities proportional to their product,
55 and taking the quotient of said ?rst and second
direct currents to .give an indication of phase
anced'modulator having'signal and carrier input '
5. An electronic circuit comprising a ?rst hal
.termlnals for respectively receiving ?rst and '
angle.
'
.
.
11. A method of measuring the phase relation
ship between two periodically varying electrical
separate means for rectifying said ?rst and second 60 quantities, comprising the'steps of modulating
one of said periodically varying electrical quan
periodically varying electrical quantities to pro
titles with the other to produce a ?rst modulated
duce corresponding ?rst and second recti?ed elec
quantity, rectifying each of said periodically
trical quantities, a second balanced modulator
varying electrical quantities to produce two non
for modulating said ?rst recti?ed electrical quan
periodically varying electrical quantities there
tity with said second recti?ed electrical quantity,
from. modulating one of said non-periodically
and means for dividing the output of said am
varying electrical quantities with the other to ,
balanced modulator by that of said‘second bal
second periodically varying electrical quantities
differing in phase from each other by an angle 0,
anced modulator to .give an indication of the
produce a second modulated quantity, and com
bining said first and second modulated quantities
6. An electronic phase determining device com 70 to give an indication of phase angle.
angle 0.
.
prising means for receiving two alternating elec
' JOHN R. WOODYA‘RD.
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